where we note that each term in the sum is computed during the update (REF ). The adaptive stopping criteria used in Algorithm  is to terminate the iterations at level \(\ell \)  whenever \(\hat{{g}}^{(\ell )}_t \le \epsilon \) .
Ideally, one would want to track the KL divergence between the SVGD approximation and the target distribution and switch to the following level once the KL divergence is below some specified threshold. However, because the normalized target density as well as the density of the SVGD approximation itself are unknown, attempting to monitor the KL divergence at each iteration is impractical.
The adaptive stopping criteria based on the gradient norm, which we use, is motivated by [1]}. It states that for small perturbations from the target density, the KL divergence between the perturbed distribution and the target distribution is asymptotically the same as the norm of the gradient squared.
